Question: Solve for $x$ and $y$ using elimination. ${-6x-y = -34}$ ${-5x+y = -21}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $-11x = -55$ $\dfrac{-11x}{{-11}} = \dfrac{-55}{{-11}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {-6x-y = -34}\thinspace$ to find $y$ ${-6}{(5)}{ - y = -34}$ $-30-y = -34$ $-30{+30} - y = -34{+30}$ $-y = -4$ $\dfrac{-y}{{-1}} = \dfrac{-4}{{-1}}$ ${y = 4}$ You can also plug ${x = 5}$ into $\thinspace {-5x+y = -21}\thinspace$ and get the same answer for $y$ : ${-5}{(5)}{ + y = -21}$ ${y = 4}$